## "Help solving - a clue"

Advanced methods and approaches for solving Sudoku puzzles

### "Help solving - a clue"

Hi This is my first post. As a new player i share similar confusion as Janiv Ratson (joined 15 June) who was advised by George (joined 20 May)in explaining "disjoint subsets" to look at cells r2c2, r2c3 and r2c6 in the following row and work out what are the only three digits that can go in these three cells:
(9), (1,5,7), (5,7), (3), (2,8,7), (1,5), (4), (5,6,7), (1,2,6.8)
iIfail to see how the chosen three candidates 1,5 and 7 would only occupy the three cells r2c2, r2c3 and r2c6 when these same candidates also occur in columns 5,8 and 9. No offence but please don't advise me it should be obvious but please explain why.
Bonsai Cec
Cec

Posts: 1039
Joined: 16 June 2005

With the candidates:
(9), (1,5,7), (5,7), (3), (2,8,7), (1,5), (4), (5,6,7), (1,2,6.8)

there are three cells that have ONLY 1, 5 and 7 as candidates between them. Three cells, with three possible candidates means that one of the candidates must occupy each cell - though we don't yet know which is which. (If you don't believe this, try allocating one of each candidate to each cell such that each digit is different - sort of a mini Sudoku with the other constraints removed.)

Since these three candidates are accounted for, they can be eliminated from the other cells, leaving
(9), (1,5,7), (5,7), (3), (2,8), (1,5), (4), (6), (2,6.8)
Last edited by simes on Sun Dec 11, 2011 9:55 am, edited 1 time in total.
simes

Posts: 324
Joined: 11 March 2005
Location: UK

[9] {157} {57} [3] {287} {15} [4] {567} {1268}

Ignoring the constraints of other columns and blocks, try putting a 7 in column 5, and thus remove the other 7's from the row.

[9] {15} {5} [3] [7] {15} [4] {56} {1268}

5 is the only candidate remaining in column 3, so remove the other 5's from the row.

[9] {1} [5] [3] [7] {1} [4] {6} {1268}

We are left with a contradiction of 1 being the only candidate remaining in each of two columns.

You will reach similar contradictions if you attempt to place a 5 or a 7 in column 8, or a 1 in column 9.

Thus, columns 2, 3, and 6 are the only columns in which the candidates 1, 5, and 7 can be.
scrose

Posts: 322
Joined: 31 May 2005

### Re: "Help solving - a clue"

(9), (1,5,7), (1,5,7), (3), (2,8,7), (1,5,7), (4), (5,6,7), (1,2,6.8)

Do you see now why those are the only three possible cells?

Also, have you looked at pairs (group of 2 numbers) and do you understand them fully? If you haven't then you should do that first.
Animator

Posts: 469
Joined: 08 April 2005